Stone Skin Unique Monsters have a 50% resistance for all types of physical attacks. In addition to 50% physical resistance, Stone Skin also doubles the monsters base defense. This means any defense modifiers it has are doubled as well.
Unique monsters with this attribute are very difficult to kill early in the game. Only a Sorceress, Druid, or a Necromancer can easily kill a Stone Skin unique in the early game with levels around 1-5 without Magic Items.
As they are merely resistant to physical attacks, the monsters will still receive damage from standard attacks. It will just take much longer to kill them; otherwise, they don't pose a greater threat than their champion counterparts.
In Diablo III, this affix returns as Extra Health. It just boosts the monster's Life pool by roughly 40%. In addition, a Shielding affix makes one monster in a group immune to damage for 5 seconds.